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Theorems · Theorem · logic and foundations

Cardinal.mk_denumerable

∀ (α : Type u) [Denumerable α], Cardinal.mk α = Cardinal.aleph0
Defined in
Mathlib.SetTheory.Cardinal.Basic
Cited by
6 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
Denumerable
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cardinal.aleph0_mul_aleph0 · cited by 4Cardinal.aleph0_mul_aleph0Cardinal.aleph0_add_aleph0 · cited by 2Cardinal.aleph0_add_aleph0MeasurableSpace.cardinal_generateMeasurableRec_le · cited by 1MeasurableSpace.cardinal_…Cardinal.mk_int · cited by 1Cardinal.mk_intFreeGroup.injective_lift_of_ping_pong · cited by 0FreeGroup.injective_lift_…Cardinal.mk_pnat · cited by 0Cardinal.mk_pnatCardinal · cited by 2598CardinalCardinal.mk · cited by 942Cardinal.mkCardinal.aleph0 · cited by 521Cardinal.aleph0Denumerable · cited by 28DenumerableCardinal.denumerable_iff · cited by 2Cardinal.denumerable_iffCardinal.mk_denumerableCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.